There are many elves in the Fellowship of the Ring, but these are the main characters.
Legolas- One of the members of the fellowship. He weilds an elvish bow and quiver, and a long white knife. He is a loyal member of the fellowship. He has a keen eye, ears, and smell. He has all of the perfections of the elves.
Galadriel- She is the Lady of Lorien. She helps the members of the fellowship by giving them a place to stay and giving them all gifts. She is one of the first elves to trust a dwarf since the Dark Days. She is very kind and beautiful.
Celeborn- Lord of Lorien. He plays but a small part in the tale of the Lord of the Rings. He helps the fellowship by giving them a place to stay and by giving them gifts.
Arwen- She does not play a part in the actual book, she is only brought up three times. You can see that there is a tale between her and Aragorn, but it is not mentioned in the book. You have to go to the appendix to look up the love story between them.
Elrond- He is Arwen's father, Lord of Rivendell. He holds the council of what is to happen to the ring in Rivendell. He is very intellectual and he is very kind.
Glorifindel- He plays a small part in the book, but he is at the Council of Elrond. He is the first to acknowledge that there are but 2 choices of what could be done with the ring. Either to be hidden and not to be mentioned again, or to take it to Mordor. He is not in the movie.